हिंदी

Determine the truth values of p and q in the following case: (p ∨ q) is T and (p ∨ q) → q is F - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F

योग
Advertisements

उत्तर

p q p ∨ q (p ∨ q) → q
T T T T
T F T F
F T T T
F F F T

Since the truth values of (p ∨ q) is T and (p ∨ q) → q is F, from the table, the truth values of p and q are T and F respectively.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३४]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 8.2 | पृष्ठ ३४

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Evaluate: ∫ x . log x dx


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]


Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

I like playing but not singing.


Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the negation of the following statement.

2 + 3 ≠ 5


Write the truth value of the negation of the following statement.

For every x ∈ N, x + 3 < 8.


Write the following statement in symbolic form.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [(~ p ∨ s) ∧ (~ q ∧ r)]


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is not holiday or Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The drug is effective though it has side effects.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

It is not true that Ram is tall and handsome.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → r


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

10 > 5 and 3 < 8


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


A biconditional statement is the conjunction of two ______ statements.


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


If q: There are clouds in the sky then p: it is raining. The symbolic form is ______


If p and q are true and rands are false statements, then which of the following is true?


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Which of the following is logically equivalent to `∼(∼p \implies q)`?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×